
These relations are also employed in the mathematical analysis of stabilized methods in Section REF . The constants in the extended stability bounds (REF ) and (REF ) depend on the order of approximation, but are independent of the background mesh size \(h\)  and the cut location. Thus, the small-cut-element problem is solved when using discontinuous Galerkin methods on aggregated meshes. Similarly, cell merging strategies in the finite volume setting have been proposed, e.g., in [1]}. Its application to the discontinuous Galerkin method can be found in [2]}, [3]}.
